I'm sure you use an edger or weed whacker to keep the grass from growing up and over the brick edging (if not, you should!) so the invading grass is probably growing under the edging and popping up in the bed. The only way to stop this from happening is to push the blade of a shovel down next the the edging to sever the creeping stolons and roots. Or, install a deeper barrier on the backside of the brick edging. Metal edging that's at least 8" wide can be hammered down into the soil on the flower bed side and it should keep new grass from invading your flower bed. Once installed (it will sever the roots and stolons as you install it), you should be able to hand pull the grass in the bed. Best wishes with your project!